Question: Rewrite as a simplified fraction. ${0.8\overline{80} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 880.808...\\ 10x &= 8.808...\end{align*}}$ Subtracting the two equations, we have: ${990x = 872}$ ${x = \dfrac{872}{990}} $ ${x = \dfrac{436}{495}} $